Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $17$ $17$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $17$ $17$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-10-21T19:36:11

Longest possible perimeter = 69.1099

Explanation:

Three angles are $\frac{5 π}{8}, \frac{π}{6}, \frac{5 π}{24}$ $(5pi)/8, pi/6, (5pi)/24$

To get the longest perimeter, side with length 17 should correspond to least angle of the triangle $(\frac{π}{6})$ $(pi/6)$

$\frac{17}{sin (\frac{π}{6})} = \frac{b}{sin (\frac{5 π}{8})} = \frac{c}{sin (\frac{5 π}{24})}$ $17 / sin (pi/6) = b / sin ((5 pi)/8) = c / sin ((5pi)/ 24)$

$b = \frac{17 \cdot sin (\frac{5 π}{8})}{sin (\frac{π}{6})} = 31.412$ $b = (17 *sin (( 5 pi)/ 8 ))/sin (pi/6 ) = 31.412$

$c = \frac{17 \cdot sin (\frac{5 π}{24})}{sin (\frac{π}{6})} = 20.698$ $c =( 17 * sin ((5 pi )/24))/sin (pi/ 6 ) = 20.698$

Perimeter $= a + b + c = 17 + 31.412 + 20.698 = 69.1099$ $= a + b + c = 17 + 31.412 + 20.698 = 69.1099$

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $17$ $17$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

Two corners of a triangle have angles of 5π8 (5 pi )/ 8 and π6 ( pi ) / 6 . If one side of the triangle has a length of 17 17 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Impact of this question

Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $17$ $17$ , what is the longest possible perimeter of the triangle?